Rumours have swirled for days about a possible breakthrough in the eastern Kharkiv region, but with no word from Ukrainian officials.
Mr Zelensky declined to name which towns had been retaken, saying that "now is not the time to name" them.
Speaking in his nightly video address to Ukrainians, President Zelensky said there was "good news" about the rumoured success of Ukrainian troops.
"I think every citizen feels proud of our soldiers," he said, naming specific military units and applauding their bravery in combat.
But he said: "Now is not the time to name the settlements to which the Ukrainian flag returns".
Ukrainian soldiers have launched an offensive south-east of Kharkiv, towards the eastern region of Donetsk, over which Russia has maintained substantial military control since the war began six months ago.
Some reports suggest Ukrainian forces may be a few dozen kilometres from the city of Izyum, an important link in Russia's military supply chain.
Speaking at an event in the United States, Colin Kahl - the Under-Secretary of Defense for Policy - suggested that Ukrainian forces were performing better than Russia in some areas.
"It is early days. I think the Ukrainians are making slow but meaningful progress. And we'll see how things pan out," he was quoted by Reuters news agency as saying.
"But I certainly think things are going better on the Ukrainian side right now in the south than is true on the Russian side."
In its nightly update, the Ukrainian General Staff said on Thursday that it had "repelled all Russian attacks" in the Kharkiv and Donetsk regions - but that both sides continued to exchange artillery and air strikes, damaging a dozen different places.